An integrator circuit is also a ________ circuit.

A simple RC integrator circuit is as shown:

Derivation:

Vi = VR + VC

VR = Voltage across the Resistor, given by:

V_R = i×R

V_C = Voltage across the capacitor

Current through the capacitor is given by:

For a large time constant RC >> 1, the above equation becomes:

Vc = V0

Obtaining the transfer function in the frequency domain:

The transfer function of the above circuit is simply the ratio of the output voltage to the input voltage and is obtained using voltage division as:

The magnitude of the above transfer function is represented as:

For ω = 0

|H(ω)| = 1

For ω = ∞

|H(ω)| = 0

This is the characteristic of a low pass filter.

We, therefore, conclude that the integrator circuit is also a low pass circuit.